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基于正切线性化控制技术和状态依赖Riccati微分方程方法,提出了一种新的非线性控制器综合策略.受正切线性化控制的启发,首先,将一类非线性系统的非线性反馈镇定问题转化为状态依赖线性时变系统的反馈镇定器设计问题.然后,给出了求解导出线性时变系统反馈镇定器设计问题的一种基于状态依赖Riccati微分方程方法.为实现该控制器的求解,仅需实时求解给定正定初始条件下的状态依赖Riccati微分方程.此外,本文所得到的解析结果还能保证非线性闭环反馈系统的指数渐近稳定性.最后,用一个数值算例验证了本文给出方法的有效性.
Based on the tangent linearization control technique and the state dependent Riccati differential equation method, a new nonlinear controller synthesis strategy is proposed.Firstly, based on the tangent linearization control, the nonlinear feedback stabilization problem for a class of nonlinear systems is transformed Is a state feedback controller design problem based on linear time-varying system.Then, a state-dependent Riccati differential equation method is proposed to solve the design problem of linear feedback systems with time-varying feedback. To solve this controller, The state-dependent Riccati differential equation for a given positive definite initial conditions must be solved in real time. In addition, the analytical results obtained in this paper can also guarantee the exponential asymptotic stability of the nonlinear closed-loop feedback system.Finally, with a numerical example, The effectiveness of the method.